{"paper":{"title":"Dimension, multiplicity, holonomic modules, and an analogue of the inequality of Bernstein for rings of differential operators in prime characteristic","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RA","authors_text":"V. V. Bavula","submitted_at":"2006-05-02T18:39:01Z","abstract_excerpt":"Let $K$ be an {\\em arbitrary} field of characteristic $p>0$ and $\\CD (P_n)$ be the ring of differential operators on a polynomial algebra $P_n$ in $n$ variables. A long anticipated {\\em analogue of the inequality of Bernstein} is proved for the ring $\\CD (P_n)$. On the way, analogues of the concepts of\n (Gelfand-Kirillov) {\\em dimension, multiplicity, holonomic modules} are found in prime characteristic (giving answers to old questions of finding such analogs).An analogue of the {\\em Quillen's Lemma} is proved for simple {\\em finitely presented} $\\CD (P_n)$-modules. In contrast to the characte"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0605073","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}